Question: Multiply and simplify the following complex numbers: $({1-4i}) \cdot ({-4+2i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({1-4i}) \cdot ({-4+2i}) = $ $ ({1} \cdot {-4}) + ({1} \cdot {2i}) + ({-4i} \cdot {-4}) + ({-4i} \cdot {2i}) $ Then simplify the terms: $ (-4) + (2i) + (16i) + (-8i^2) $ Imaginary unit multiples can be grouped together. $ -4 + (2 + 16)i - 8 i^2 $ After we plug in $i^2 = -1$, the result becomes $ -4 + (2 + 16)i - (-8) $ The result is simplified: $ (-4 + 8) + (18i) = 4+18i $